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Extreme EventsCost-Effectiveness Analysis

Scott MatthewsCourses: 12-706 / 19-702

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Admin

HW 4 Solutions Out (some late)Project 2 Coming out soon.

Due Friday Nov 17th

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Extreme Events

So-called low-probability, high-consequence events Natural disasters (eg Hurricanes) Catastrophic infrastructure failure

Modeling them requires just doing good sensitivity analysis On risk tolerance / utility

“how risk averse do you need to be for it to matter?” On expected losses (consequences)

“how much would you have to lose for it to matter?”

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Relevant Thoughts

As you (the decision maker) becomes more risk averse, you tend to worry ONLY about the worst case

Example: using exponential utility (similar to Deal or No Deal) Recall definition of R parameter in function Equally willing to risk winning R or losing R/2 For individuals, generally R ~ $1000s Recall goal is to maximize CE

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Exponential Utility Function u(x)=1-exp(-x/R)

-

0.20

0.40

0.60

0.80

1.00

1.20

$- $3,000,000 $6,000,000 $9,000,000 $12,000,000

$ amount

Utility

R=1,000,000 R=2,000,000 R=3,000,000

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Exponential Utility Function u(x)=1-exp(-x/R)

(2.00)

(1.50)

(1.00)

(0.50)

-

0.50

1.00

$(4) $(1) $2 $5 $8 $11 $14 $17 $20Millions

$ amount

Utility

R=1,000,000 R=2,000,000 R=3,000,000

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Example: Infrastructure Failure

Probability (P) of happening: About 0.5%

Damage (D) if occurs - $100 millionTypical EMV = P*D = $1000sThis obviously is not the right method

Saw similar result in project 1

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Utility

Recall: eliciting and using individual utility functions to make decisions

Is there a similar concept to help us make decisions at the social level?

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Specifics on Saving Lives

Cost-Utility Analysis Quantity and quality of lives important

Just like discounting, lives are not equal Back to the developing/developed example

But also: YEARS are not equal Young lives “more important” than old Cutting short a year of life for us vs Cutting short a year of life for 85-year-old Often look at ‘life years’ rather than ‘lives’

saved.. These values also get discounted

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Contingent Valuation

Analysis method used when there is no observable market Example: water quality at national parks Asks questions to population Is a last resort option! Called ‘contingent’ since you never

really pay Valuing use non-controversial Valuing ‘non-use’ VERY controversial

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Example

Asked for valuations of a certain good Then estimate overall WTP for it -

similar to travel time demand functions Extrapolated to entire population Assumes random sample!

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Criticisms of CV

Extrapolation of ‘all CV studies’ to average consumer would take over their budget

Normal statistical problems (sampling, non-response, biases, etc.)

Surveying opinions is impreciseProblems tend to be complicated

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WTP versus WTA

Economics implies that WTP should be equal to ‘willingness to accept’ loss

Turns out people want MUCH MORE in compensation for losing something

WTA is factor of 4-15 higher than WTP! Also see discrepancy shrink with

experience WTP formats should be used in CVs Only can compare amongst individuals

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Measuring Lives Saved

Life years (prevented fatalities) not equal Qualitative and quantitative issue Need to consider tradeoffs

Simple example Status quo: no newborns survive a condition Alt. A: 5 live, but with permanent disability Alt. B: 2 live, but with low levels of disability

Which option (SQ, A, B) is preferable?Assume Y increasing, H increasing

Equal costs, no relevant uncertainty

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Simple Example

Measure of TotalAdditional Years

HealthStatus

Y1 Y2 Y3

H1 Y1H1SQ Y2H1 Y3H1

H2 Y1H2 Y2H2 Y3H2B

H3 Y1H3 Y2H3A Y3H3

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The Quality/Quantity Game

Assume “preference” for Increased number of years lived Increased level of health Would your preferences be the same?

If so, SQ “dominated” by both A and B Note different horizontal/vertical preference But which of A or B is better? We all understand difference in years Need an index of health status

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Health Status Index

Death

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SeverelyDisabled

MinimallyDisabled

HealthModeratelyDisabled

0.15 0.47 0.92 1

Measures utility, derived from expertsBut this says nothing about tradeoff!

Can perform tradeoff survey Value of “shorter Y, higher H” vs. opposite

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Methods

Health Rating method (see above)Time tradeoff methodStandard gamble methodDiscounting life years

Can/should we discount them? Unlike cash values, we can’t make a

decision to trade 1 year today for 10 yrs from now

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Cost-Effectiveness TestingGenerally, use when:

Considering externality effects or damagesCould be environmental, safety, etc.

Benefits able to be reduced to one dimension Alternatives give same result - e.g. ‘reduced x’ Benefit-Cost Analysis otherwise

difficult/impossible

Instead of finding NB, find “cheapest” Want greatest bang for the buck

Find cost “per unit benefit” (e.g. lives saved) Allows us to NOT include ‘social costs’

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Why CEA instead of CBA?

Similar to comments on MCDM Constraints may limit ability to performMonetizing maybe difficult or

controversial Easy to find lives saved, hard to judge

valueMonetizing can’t capture total social value or

distorts its value

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The CEA ratiosCE = C/E

Equals cost “per unit of effectiveness” e.g. $ per lives saved, tons CO2 reduced Want to minimize CE (cheapest is best)

EC = E/C Effectiveness per unit cost e.g. Lives saved per dollar Want to maximize EC

No practical difference between 2 ratios

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An Obvious Example

AlternativesValuesA B C

Cost $10 M $10 M $10 M# LivesSaved

5 10 15

CEratio

$2 M $1 M $0.67M

ECratio

0.5life

1 life 1.5lives

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Another Obvious One

AlternativesValuesA B C

Cost $5 M $10 M $15 M# Lives Saved 10 10 10CE ratio($M/life)

$0.5 $1 $1.5

EC ratio(life/$M)

2 1 0.66

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Comments on Obvious Examples

Each had 2 dominated alternativesCould easily identify best CE/EC

optionAlso had fixed scale

Fixed cost scale in first Fixed effectiveness in second

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Interesting Example

AlternativesA B

Cost $1 M $100 M# LivesSaved

4 200

CE ratio $250k $500kEC ratio 4 lives 2 lives

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Lessons Learned

Ratios still tend to hide results Do not take into account scale issues CBA might have shown Option B to be better (more lives

saved) Tend to only consider budgetary costs CEA used with constraints? Minimize C s.t. E > E*

Min. effectiveness level (prev slide) Find least costly way to achieve it

Minimize CE s.t. E > E* Generally -> higher levels of C and E!

Can have similar rules to constrain cost

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Sample Applications

Cost-effectiveness of: New drug/medical therapies* very

popular Pollution prevention Safety regulations

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Definitions

Overall cost-effectiveness is the ratio of the annualized cost to the quantity of effectiveness benefit.

Incremental cost-effectiveness is the difference in costs divided by the difference in effectiveness that results from comparing one option to another, or to a benchmark measure.

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Incremental CE

To find incremental cost-effectiveness : Sort alternatives by ‘increasing effectiveness’ TAC = total annualized cost of compliance PE = effectiveness (e.g. benefit measure) CE = (TACk – TACk-1) / ( PEk – PEk-1) CE = incremental cost-effectiveness of Option k Use zero values (if applicable) for base case

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Incremental CE Example

Inc CE here only relevant within control categories (metals v. oils v. org’s) ** Negative CE means option has more removals at lower cost Source: US EPA Office of Water EPA 821-R-98-018, “Cost Effectiveness Analysis of Effluent Limitations

Guidelines and Standards for the Centralized Waste Treatment Industry”

Control Option Name Costs Removals Cost- Incremental(pounds) Effectiveness CE

Metals 2 $8,853,173 369,112 $24 $24Metals 4 $1,843,303 372,040 $5 -$2394.08**Metals 3 $9,179,935 379,571 $24 $974Oils 8 $313,523 13,943 $22 $22Oils 9 $313,523 14,811 $21 $0Organics 4 $150,694 —Organics 3 $275,074 27,055 $10 $10

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Definitions (2)

Marginal cost-effectiveness refers to the change in costs and benefits from a one-unit expansion or contraction of service from a particular intervention (e.g. an extra pound of emissions, an extra fatality avoided).

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Why is CEA so relevant for public policy analysis?

Limited resources!Opportunity cost of public spending

i.e. if we spend $100 M with agency A, its $100 M we cannot spend elsewhere

There is no federal rule saying ‘each million dollars spent must save x lives’

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Gray Areas

How to measure cost-effectiveness when there is a single project cost but multiple effectiveness categories E.g. fatalities and injuries, CO2 and SO2

Alternatives: Keep same cost, divide by each benefit

Overstates costs for each Keep same cost, divide by ‘sum of benefits’ Allocate cost, divide by each benefit separately Weight the costs and/or benefits

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Another CEA Example

Automated defribillators in community http://www.early-defib.org/03_06_09.ht

ml What would costs be? What is effectiveness?